8006 PRMIA Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition Free Practice Exam Questions (2025 Updated)

Macaulay duration is the weighted average of the present value of payments received on a bond, weighted by the year in which the payments are received. If the yield curve changes shape, it will change the present values of the coupons and therefore also the Macaulay duration. Statement I is therefore not correct. However, if the bond were to be a zero-coupon bond, changes in the curve will not affect its duration so long as the interest rate at maturity stays constant.

Modified duration = Macaulay Duration/(1 + rate/compounding frequency). Therefore modified duration will change if the compounding frequency changes, assuming the nominal rate of interest for the coupons are identical. Therefore statement II is correct.When rates are expressed as continuously compounded rates, modified duration and Macaulay duration will be identical. This intuitively follows from the formula for modified duration: Modified duration = Macaulay Duration/(1 + rate/compounding frequency). For continuously compounded rates, the compounding frequency approaches infinity, so the denominator approaches 1, leaving modified duration equal to the Macaulay duration. Therefore statement III is correct.

Convexity is higher for a bond that has its payments spread out compared to a bond that has its payments concentrated at a single point in time. For a bond with a higher coupon, the higher coupons have the effect of spreading the present value of the bond over a longer period, when compared to a bond with lower coupons where the payment is comparatively more concentrated at the maturity. Therefore Convexity is higher for a bond with a lower coupon when compared to a similar bond with a higher coupon. Statement IV is not correct.

To answer this question, we need to look at the put-call parity, which can be expressed as:

Value of call - Value of put = Spot price - Exercise price discounted to the present

or, Value of call - Value of put = Stock - Bond with a future value equal to exercise price

Therefore, a long call and a short put is equivalent to a long stock position and a short bond.

Choice 'a' is therefore the correct answer. (Alternatively, we could also have constructed a graph of the payoff profiles to arrive at the same answer).

Statement I is correct - since forward prices are determined as (Spot - PV of dividends)*e^(rt), an increase in dividends will reduce forward prices.

Statement II is incorrect as forward prices will be determined by near term interest rates, specifically by the borrowing rate for the period of the contract, and will stay unchanged if near term interest rates do not change.

Statement III is incorrect. Futures exchanges require both buyers and sellers to deposit initial margins as prices can move adversely for either of them.

Statement IV is incorrect, as the margin deposited when a contract is entered into is called initial margin. Margin calls thereafter resulting from movements in prices are called variation margin.

Statement V is incorrect. Most futures exchanges distinguish between hedgers and speculators and require different margins from each.

Statement VI is incorrect. Interest rate futures behave almost identically to their bond counterparts, and carry both duration and convexity.

Treasury bond futures do not specify which bond can be used to effect delivery, but allow the seller to pick from a number of available bonds. As a result, one of these eligible bonds emerges as being the 'cheapest' to deliver, and this CTD bond is determined by the basis between the cash price of the bond and the futures spot price as adjusted by the conversion factor for this specific bond. (ie, basis = Cash Price of the Bond - (Futures Price x Conversion Factor).)

The bond with the lowest basis is generally the CTD. In the given question, the three basis calculations are:

1) 97 - (0.9 x 105) = 2.5

2) 101 - (1 x 105) = -4

3) 106 - (1.1 x 105) = -9.5

Since the third bond with a quote of 106 has the lowest basis, Choice 'b' is the correct answer.

The day count convention used for US treasury bonds is Act/Act. The other choices are incorrect.